Question: Multiply the following complex numbers: $({3i}) \cdot ({i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3i}) \cdot ({i}) = $ $ ({0} \cdot {0}) + ({0} \cdot {1}i) + ({3}i \cdot {0}) + ({3}i \cdot {1}i) $ Then simplify the terms: $ (0) + (0i) + (0i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 0)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 0)i - 3 $ The result is simplified: $ (0 - 3) + (0i) = -3 $